Walk up to her. Be like "Hey, would you want to go to prom with me?". At least, that's what I did for my first prom, worked fairly well. If you're already dating I don't really know since my second prom I went with my girlfriend and it was just like "We're together, we're going."... But I'm also very, very, uncreative and I already knew that girl would say yes since we were insanely close.

how about take a pict of yourself holding a note: want to go to prom with me?
print it out and glue it to some cartboard orso.
now cut it up in little pieces and give it to her, she can puzzle it first lol